Question: What is the measure of the smaller angle between the hands of a 12-hour clock at 12:25 pm, in degrees? Express your answer as a decimal to the nearest tenth.
Solution: Every minute, the minute hand moves $360 \div 60 = 6$ degrees. At 25 minutes past the hour, the minute hand is $25 \times 6 = 150$ degrees past the vertical 12:00 position. Every minute, the hour hand moves $360 \div 12 \div 60 = 0.5$ degrees. At 25 minutes past 12:00, the hour hand is $25 \times 0.5 = 12.5$ degrees past the vertical 12:00 position. The angle between the hands of the clock at 12:25 is $150 - 12.5 = \boxed{137.5\text{ degrees}}$.

[asy]
unitsize(2.5 cm);

int i;

draw(Circle((0,0),1));

for (i = 0; i <= 11; ++i) {
  draw(0.9*dir(30*i)--dir(30*i));
  label("$" + string(i + 1) + "$", 1.15*dir(90 - 30*i - 30));
}

draw((0,0)--0.8*dir(300));
draw((0,0)--0.6*dir(90 - 12/25*30));
[/asy]